Construction of interacting quantum field theory in four dimensions remains one
of the most important open problems in mathematical physics. Further steps toward
higher dimensions within the above operator-algebraic approach have been obtained
[1]}, [2]}, however, the second step to find localized observables
has so far turned out to be unsuccessful [1]}.
Furthermore, we found that conformal covariance implies triviality of scattering in two
dimensions [4]} yet it is possible to construct weakly localized,
conformally covariant models [5]}. Thus construction of weakly
localized models should be considered as an important but intermediate step.
